For spectrally negative branching Lévy processes with absorption, the tail probability that at least n particles hit zero decays like a power of n in the subcritical case and like 1/(n log^2 n) in the critical case.
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Total progeny for spectrally negative branching L{\'e}vy processes with absorption
For spectrally negative branching Lévy processes with absorption, the tail probability that at least n particles hit zero decays like a power of n in the subcritical case and like 1/(n log^2 n) in the critical case.